This study proposes transformation functions and matrices between coefficients in the original and reparameterized parameter spaces for an existing linear-linear piecewise model to derive the interpretable coefficients directly related to the underlying change pattern. Additionally, the study extends the existing model to allow individual…

Applied researchers faced with limited resources can utilize planned missing designs by incorporating missing data into their research design to collect more and higher quality data compared to a conventional experimental design. Two-method measurement planned missing designs (TMM-PMD) are a type of planned missing design whereby researchers…

Growth mixture models (GMMs) are a popular method to identify latent classes of growth trajectories. One shortcoming of GMMs is nonconvergence, which often leads researchers to apply covariance equality constraints to simplify estimation, though this may be a dubious assumption. Alternative model specifications have been proposed to reduce…

Assessing student achievement over multiple years is complicated by students' annual matriculation through different classrooms. The process of matriculation, or annual classroom change, threatens the validity of statistical inferences because it violates the independence of observations necessary in a regression context. The current study…

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the…

Typical longitudinal growth models assume constant functional growth over time. However, there are often conditions where trajectories may not be constant over time. For example, trajectories of psychological behaviors may vary based on a participant's age, or conversely, participants may experience an intervention that causes trajectories to…

The piecewise latent growth models (PWLGMs) can be used to study changes in the growth trajectory of an outcome due to an event or condition, such as exposure to an intervention. When there are multiple outcomes of interest, a researcher may choose to fit a series of PWLGMs or a single parallel-process PWLGM. A comparison of these models is…

Education experiments frequently assign students to treatment or control conditions within schools. Longitudinal components added in these studies (e.g., students followed over time) allow researchers to assess treatment effects in average rates of change (e.g., linear or quadratic). We provide methods for a priori power analysis in three-level…

Sources of longitudinal achievement data are increasing thanks partially to the expansion of available interim assessments. These tests are often used to monitor the progress of students, classrooms, and schools within and across school years. Yet, few statistical models equipped to approximate the distinctly seasonal patterns in the data exist,…

The latent growth model (LGM) in structural equation modeling (SEM) may be extended to allow for the modeling of associations among multiple latent growth trajectories, resulting in a multiple domain latent growth model (MDLGM). While the MDLGM is conceived as a more powerful multivariate analysis technique, the examination of its methodological…

While states are no longer required to set up teacher evaluation systems based in significant part on student test scores, quite a few continue to use value-added (VAMs) or student growth percentile (SGP) models for that purpose. In this study, we analyzed three years of teacher data to illustrate the performance of teachers' median growth…

This study investigated the optimal strategy for model specification search under the latent growth modeling (LGM) framework, specifically on searching for the correct polynomial mean or average growth model when there is no a priori hypothesized model in the absence of theory. In this simulation study, the effectiveness of different starting…

The purpose of this study is extend previous methods by Raudenbush and Liu (2001) and Spybrook et al. (2011), and provide methods for power analysis of tests of treatment effects in studies of polynomial change with two levels of nesting (e.g., students and schools) where the treatment is either at the third level (e.g., school intervention) or at…

Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This…

Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due…